Overpartition Statistics

Many partition results and $q$-series identities are classically derived through analytical techniques, though the results beg for a combinatoric interpretation. -- the standard examples being the Ramanujan congruences. Historically, the combinatorics were filled in by studying integer valued functions on the set of partitions, namely the rank and the crank functions.

We show how the ordinary partition statistics can be extended into the more general overpartition case.